All Questions
Tagged with derivations fa.functional-analysis
7 questions
7
votes
3
answers
2k
views
A question on fractional derivatives
I know practically nothing about fractional calculus so I apologize in advance if the following is a silly question. I already tried on math.stackexchange.
I just wanted to ask if there is a notion of ...
user168611
5
votes
1
answer
264
views
Counter example for Hadamard Differentiability
I am having a hard time while trying to fully understand Hadamard differentiability.
I use the following definition taken from a German source ( Martin Brokate, "Konvexe Analysis und ...
- 53
1
vote
2
answers
435
views
Prove a $C^{\infty}$ multivariable function is lipchitz via Jacobian matrix [closed]
I would like to prove a real $C^{\infty}$(polynomial) multivariable function $F : (a_1,a_2,...a_n) \rightarrow (b_1,b_2,...b_n) $ is lipchitz of parameter $l$
is it sufficient to prove the norm of ...
- 159
1
vote
1
answer
107
views
Derivatives and exponential derivatives quotient operators on two variables
I consider for example the following function of two variables given by
$$f(x,y)=\sum_{n=0}^{+\infty}\frac{\delta_{x}^{-m} \exp(\delta_{x})}{\delta_{y}^{-m}\exp(\delta_{y})}\left(\frac{x}{y}\right)^{n}...
- 159
1
vote
0
answers
245
views
A characterization of the integral
Let $I(f)$ be an endomorphism of the smooth functions with zero value in zero such that:
$$\ln[1+I(f)]=I\left(\frac{f}{1+I(f)}\right).
$$
Then, does it exist $g$ smooth such that:
$$I(f)(x)=\int_0^x f(...
- 377
1
vote
0
answers
89
views
Derivation in Sobolev space [closed]
Let $f\in W^{1,\infty}(]0,T[)$ $(0<T\le\infty)$ such that
$f(x)>0$ a.e. $x\in\mathopen]0,T[$ and let
$$g(x)=e^{-\int_0^x \frac{ds}{f(s)}}$$
Formally $g' = -\frac{1}{f}g$.
How can I justify this ...
- 19
0
votes
0
answers
36
views
Derivate involving Bessel function of second type
Let.
$$f := (x, y) \mapsto \text{BesselK}(1, c \cdot (a - b \cdot (x + y))) \cdot \exp(c \cdot b \cdot (y - x))$$
Is there a close formula for this $$\frac{\partial^{m+n}}{\partial y^m \partial x^n} f(...
- 109